I believe the general rule is all protruding parts must fit within those dimensions.

However, I've never seen check-in staff meaure regular-shaped baggage. They only get worried about fragile items, overweight items, odd-shaped items, chemicals etc. If it goes on the conveyor, they don't seem worried. In the UK, a single piece cannot be more than 32Kg (for the safety of baggage handlers) so if your luggage allowance is 40Kg, then you would have to take two pieces to use it. If you've maxed out on the size, its easy to to go above 32Kg.

I just measured a suitcase I regularly use. External dimensions add up to 63" and its not the biggest I use. I use a variety of airlines but not LH.

I think you'll be fine with 64", especially as the dimensions are in proportion (ie its not an odd shape).

Maybe worth asking this in the LH forum in case LH are particularly fussy. (Or ask the mods to move the thread.)